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SageMath
E = EllipticCurve("bi1")
E.isogeny_class()
Elliptic curves in class 154938.bi
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
154938.bi1 | 154938x2 | \([1, 0, 1, -41662, 3269564]\) | \(23314974828101839/322524\) | \(110625732\) | \([2]\) | \(327680\) | \(1.0987\) | |
154938.bi2 | 154938x1 | \([1, 0, 1, -2602, 51020]\) | \(-5676903560719/21172752\) | \(-7262253936\) | \([2]\) | \(163840\) | \(0.75210\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 154938.bi have rank \(1\).
Complex multiplication
The elliptic curves in class 154938.bi do not have complex multiplication.Modular form 154938.2.a.bi
sage: E.q_eigenform(10)
Isogeny matrix
sage: E.isogeny_class().matrix()
The \(i,j\) entry is the smallest degree of a cyclic isogeny between the \(i\)-th and \(j\)-th curve in the isogeny class, in the LMFDB numbering.
\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.